Mean (Average)
The mean, often referred to as the arithmetic average, is one of the most fundamental measures of central tendency. It summarizes a dataset by representing all values with a single balanced number.
Core Definition
The mean is obtained by adding all numerical values in a dataset and dividing the total by the number of observations.
Each value contributes equally to the final result. Because of this equal contribution, the mean reflects the overall balance of the data.
Conceptual Interpretation
The mean can be understood as a redistribution process. If all values were evenly redistributed, each would become equal to the mean.
This interpretation explains why extreme values can significantly shift the result: large or small observations affect the total sum before division.
Limitations
Although widely used, the mean has important limitations:
- It is sensitive to outliers.
- It does not apply to categorical data.
- It may misrepresent heavily skewed distributions.
In skewed datasets, the median often provides a more representative measure.
Position Within Central Tendency
The mean is one of three primary measures used to describe the center of data:
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